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D.4.5.13 primdecEHV
Procedure from library ehv.lib (see ehv_lib).
- Usage:
- primdecEHV(I [,Strategy]); I ideal, Strategy list
- Return:
- a list pr of primary ideals and their associated primes:
pr[i][1] the i-th primary component,
pr[i][2] the i-th prime component.
- Note:
- Algorithm of Eisenbud/Huneke/Vasconcelos.
The (optional) second argument determines the strategy used:
Strategy[1] > strategy for equidimensional part
= 0 : uses equiMaxEHV
= 1 : uses equidimMax
Strategy[2] > strategy for equidimensional radical
= 0 : uses equiRadEHV, resp. radicalEHV
= 1 : uses equiRadical, resp. radical
Strategy[3] > strategy for equiRadEHV
= 0 : combination of strategy 1 and 2
= 1 : computation of the radical just with the
help of regular sequences
= 2 : does not try to find a regular sequence
Strategy[4] > strategy for the computation of ideal quotients
= n : uses quot(.,.,n) for the ideal quotient computations
If no second argument is given then Strategy=(0,0,0,0) is used.
Example:
| LIB "ehv.lib";
ring r = 0,(x,y,z),dp;
poly p = z2+1;
poly q = z3+2;
ideal i = p*q^2,y-z2;
list pr = primdecEHV(i);
pr;
==> [1]:
==> [1]:
==> _[1]=z2-y
==> _[2]=y4+y3+4y2z+4yz+4y+4
==> [2]:
==> _[1]=z2-y
==> _[2]=y2z+yz+2y+2
==> _[3]=y3+y2+2yz+2z
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